Forecasting electrical power usage can be desirable to an entity for planning and budgetary purposes. For example, a manufacturer may desire to forecast power usage for a factory to determine an amount of money to budget for such usage. Similarly, a company may desire to forecast its power usage in order to negotiate a rate contract with a utility supplying the electrical power.
Demand for electrical power (the energy usage, or load, on the electrical system) at any point in time is dependent upon weather factors such as temperature, humidity, wind, and precipitation (with reducing dependence in the order specified and temperature affecting the load most significantly). Load is also influenced by other factors such as the day of the week, or if the day is a holiday or other day of atypical load. For example, a factory likely will demand a higher load on a work day, when it is producing goods, and demand a lower load on weekends and holidays when there is no production. Using regression methods it is possible to identify a mathematic relationship that allows the load to be forecasted if a forecasted temperature at a specific time is known. The accuracy of the forecast can be increased if other factors such as the humidity and any special characteristics of the day (e.g., the day of the week, holiday, etc.) are taken into account in selecting reference data points (e.g., reference days).
Since statistical methods are used to create the model that would represent the relationship between load and temperature, the accuracy of the model depends upon not only the number of data points used to create the model but also the statistical relevance of those data points to the model. The accuracy of a load data forecast depends upon the accuracy of the statistical model developed to represent a relationship between load and temperature. The accuracy of the statistical model in turn depends upon the quality of the reference days used to create the model.
Reference days may have similar overall humidity profiles to the day to be forecasted (as determined by correlating humidity measurements of a reference day to predicted humidity values of the day to be forecasted). However the reference days may have extremely different humidity values and hence may not be good predictors for the day to be forecasted. Also, it may be difficult or impossible to differentiate one reference day from another in terms of its quality as a predictor based only on a correlation coefficient with respect to the day to be forecasted. For example, a group of reference days with humidity profiles similar to the day to be forecasted may fall into any of the following categories:                very similar humidity values and very similar humidity profile to the day to be forecasted;        somewhat similar humidity values and somewhat similar humidity profiles to the day to be forecasted; and        similar overall humidity profiles but extremely different humidity values to day to be forecasted.        
Reference days with very similar humidity values and very similar humidity profiles to the day to be forecasted are the best predictors to use in developing a model to forecast load data. Reference days with somewhat similar humidity values and somewhat similar humidity profiles to the day to be forecasted can be useful to develop the model, but only if a large enough number of reference days with very similar humidity values and very similar humidity profiles cannot be found. However it is difficult to differentiate between these three categories, as a humidity profile only gives a linear trend of the humidity values of a historical day compared to the day to be forecasted. Individual humidity values of the historical day can be very dissimilar to a corresponding humidity value of the day to be forecasted, even if the overall linear trends are similar. What is needed is a way to differentiate between reference days with very similar humidity values and profiles from days with somewhat similar humidity values and profiles, as well as a way to exclude days with similar humidity profiles and extremely dissimilar humidity values. The present disclosure is directed to addressing these and other needs and solving these and other problems.